Matrix: Mittelmann/nug08-3rd

Description: LP lower bounds for quadratic assignment problems

Mittelmann/nug08-3rd graph
(bipartite graph drawing)


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  • download as a MATLAB mat-file, file size: 312 KB. Use UFget(1645) or UFget('Mittelmann/nug08-3rd') in MATLAB.
  • download in Matrix Market format, file size: 531 KB.
  • download in Rutherford/Boeing format, file size: 390 KB.

    Matrix properties
    number of rows19,728
    number of columns29,856
    structural full rank?yes
    structural rank19,728
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorS. Karisch, F. Rendl
    editorH. Mittelmann
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 19728-by-1
    cfull 29856-by-1
    lofull 29856-by-1
    hifull 29856-by-1
    z0full 1-by-1


    Hans Mittelmann test set,           
    minimize c'*x, subject to A*x=b and lo <= x <= hi                      
    NUG:  computing LP lower bounds for quadratic assignment problems.  see
    S.E. KARISCH and F. RENDL. Lower bounds for the quadratic assignment   
    problem via triangle decompositions.  Mathematical Programming,        
    71(2):137-152, 1995.                                                   
    K.G. Ramakrishnan, M.G.C. Resende, B. Ramachandran, and J.F. Pekny,    
    "Tight QAP bounds via linear programming," Combinatorial and Global    
    Optimization, P.M. Pardalos, A. Migdalas, and R.E. Burkard, eds.,      
    World Scientific Publishing Co., Singapore, pp. 297-303, 2002.         

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD184,473,912
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD114,635,182

    SVD-based statistics:
    null space dimension1,458
    full numerical rank?no
    singular value gap2.98861e+13

    singular values (MAT file):click here
    SVD method used:s = svd (full (R)) ; where [~,R,E] = spqr (A') with droptol of zero

    Mittelmann/nug08-3rd svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.